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       LAPACK - library of linear algebra routines

什麼是 LAPACK ?

    LAPACK      是一個      Fortran      77      子程序的      transportable      library      ,
    用來解決多數數字線性代數中共同的問題: systems of  linear  equations,  linear  least  squares
    problems,       eigenvalue       problems,       還有      singular      value      problems.

    LAPACKLINPACKEISPACK 的後繼者。 它擴展了這些庫的功能,包含了線性系統的 equilibration,
    iterative  refinement,  error  bounds,  和  driver  routines, routines for computing and re-
    ordering  the  Schur  factorization,  還有  condition  estimation  routines  for  eigenvalue
    problems.   LAPACK  通過包含  finding  singular  values  and  eigenvalues  of  bidiagonal and
    tridiagonal matrices respectively  that  arise  in  SVD  and  symmetric  eigenvalue  problems
    的高精度算法提高了                         EISPACK                         中標準算法的精度。
    這些算法和軟件被重新編寫,在向量處理器上,高性能          ``superscalar''          工作站上和
    共享內存的多處理器上都可以獲得高效率。 LAPACK 軟件還附帶了一個複雜的測試和時間測算套件。


    完整的  LAPACK 軟件包可以從 xnetlib 和 NAG 得到,也可以從 netlib 獲得特定的庫。 要查看 LAPACK
    內容的描述,向 發一封消息類型爲: send index from lapack 的電子郵件。

    Xnetlib is an X-version of netlib recently developed at the University of Tennessee  and  Oak
    Ridge National Laboratory.  Unlike netlib, which uses electronic mail to process requests for
    software and other text, xnetlib uses an X Window graphical user interface and a socket-based
    connection  between  the  user's  machine  and the xnetlib server machine to process software
    requests. The complete contents of LAPACK is available in tar/compress format from xnetlib.

    To receive  a  copy  of  xnetlib  send  the  message  "send  xnetlib.shar  from  xnetlib"  to

    When you receive the shar file, remove the mail header, save it to a file, type 'sh filename'
    and follow the instructions in the README file.

    Alternatively, the complete LAPACK package can be obtained from NAG on magnetic media  for  a
    handling charge.  For further details contact NAG at one of the following addresses:

    NAG Inc                         NAG Ltd              NAG GmbH
    1400 Opus Place               Wilkinson House      Schleissheimerstrasse 5
    Suite 200                     Jordan Hill Road     W-8046 Garching bei Munchen
    Downers Grove, IL 60515-5702  Oxford OX2 8DR       Germany
    USA                           England
    Tel: +1 708 971 2337          Tel: +44 865 511245  Tel: +49 89 3207395
    Fax: +1 708 971 2706          Fax: +44 865 310139  Fax: +49 89 3207396

    LAPACK  has been thoroughly tested, on many different types of computers.  The LAPACK project
    supports the package in the sense that reports  of  errors  or  poor  performance  will  gain
    immediate   attention   from  the  developers.  Such  reports,  descriptions  of  interesting
    applications, and other comments should be sent by electronic mail to


    The LAPACK Users' Guide is published by SIAM and was made available May, 1992.  LAPACK Users'
    Guide gives an informal introduction to the design of the algorithms and software, summarizes
    the contents of the  package,  and  describes  the  conventions  used  in  the  software  and
    documentation,  and  includes  complete  specifications for calling the routines.  The LAPACK
    Users' Guide can be purchased from: SIAM; 3600 University City Science Center;  Philadelphia,
    PA  19104-2688;  215-382-9800, FAX 215-386-7999.  It will also be available from booksellers.
    The Guide costs $15.60 for SIAM members, and $19.50 for non-members.   Please  specify  order
    code OT31 when ordering.  To order by email, send email to

    A  list  of  known  problems, bugs, and compiler errors for LAPACK, as well as errata for the
    LAPACK Users' Guide and the LAPACK code itself, is maintained on netlib.  For a copy of  this
    report,  send  email  to with a message of the form: send release_notes from


    A number of working notes were written during the development  of  LAPACK  and  published  as
    LAPACK Working Notes, initially by Argonne National Laboratory and later by the University of
    Tennessee.  Many of these reports have subsequently appeared as journal  articles.   Most  of
    these  working  notes  are  available  in  postscript form from netlib.  To receive a list of
    available reports, send email to with a message of the form: send index  from
    lapack/lawns.   Otherwise,  requests  for  copies  of  these working notes can be sent to the
    following address.

    LAPACK Project  c/o  J.J.  Dongarra  Computer  Science  Department  University  of  Tennessee
    Knoxville, Tennessee 37996-1301 USA Email:


    LAPACK  has  been  funded in part by NSF, DOE, and DARPA, with developmental support from NAG
    Ltd., Cray Research, and many friends and colleagues around the world.

    Ed Anderson, Zhao-jun Bai, Chris Bischof, Jim Demmel, Jack Dongarra,  Jeremy  Du  Croz,  Anne
    Greenbaum, Sven Hammarling, Alan McKenney, Susan Ostrouchov, and Danny Sorensen

                 (           l    l    l    l )
                 (           a   -a    a   -a )
           1/4 * ( p    p             -p   -p )
                 ( a   -a             -a    a )
                 ( c    c   -c   -c           )
                 ( k   -k   -k    k           )


    The  name  of  each  LAPACK routine is a coded specification of its function (within the very
    tight limits of standard Fortran 77 6-character names).

    All driver and computational routines have names of the form XYYZZZ, where  for  some  driver
    routines the 6th character is blank.

    The first letter, X, indicates the data type as follows:

          S  REAL
          C  COMPLEX
          Z  COMPLEX*16  or DOUBLE COMPLEX

    The  next  two  letters, YY, indicate the type of matrix (or of the most significant matrix).
    Most of these two-letter codes  apply  to  both  real  and  complex  matrices;  a  few  apply
    specifically to one or the other.

    The  last  three  letters  ZZZ  indicate the computation performed.  For example, SGEBRD is a
    single precision routine that performs a bidiagonal reduction (BRD) of a real general matrix.


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